Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Stokes-operator-squeezed continuous-variable polarization states

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincare sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

A economia portuguesa e as alterações climáticas - uma abordagem sectorial - aproximação ou divergência com a economia espanhola?

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Gestão e Políticas Ambientais

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Una aproximación sectorial a la localización industrial en Cataluña

El objetivo de este estudio es analizar las decisiones de localización de las actividades industriales desde una óptica sectorial. En concreto, se explica la distribución municipal en Catalunya del número de nuevas inversiones procedentes del Registro de Establecimientos Industriales, durante el período 1986-2000. Los determinantes de la localización industrial se han agrupado en tres categorías: condiciones de oferta de factores, economías de aglomeración y accesibilidad. El análisis se lleva a cabo utilizando un modelo de eventos discretos con datos de panel. Los resultados obtenidos muestran que los tres conjuntos de variables introducidas son relevantes en la explicación de la localización de las empresas manufactureras y que actúan en diferente grado para los diferentes sectores.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

"Vegeu el resum a l'inici del document del fitxer adjunt."

Large deviation for BSDE with subdifferential operator

In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle.

Simulating the Impact of Sectorial Productivity Gains on Two Regional Economies: Key Sectors from a Supply Side Perspective

In this paper we simulate and analyse the economic impact that sectorial productivity gains have on two regional Spanish economies (Catalonia and Extremadura). In particular we study the quantitative effect that each sector’s productivity gain has on household welfare (real disposable income and equivalent variation), on the consumption price indices and factor relative prices, on real production (GDP) and on the government’s net income (net taxation revenues of social transfers to households). The analytical approach consists of a computable general equilibrium model, in which we assume perfect competition and cleared markets, including factor markets. All the parameters and exogenous variables of the model are calibrated by means of two social accounting matrices, one for each region under study. The results allow us to identify those sectors with the greatest impact on consumer welfare as the key sectors in the regional economies. Keywords: Productivity gains, key sectors, computable general equilibrium

On a supremum operator

Vegeu el resum a l'inici del document del fitxer adjunt.